Hand Out  --  Keynesian Cross Model (Income Expend. Model)

( a slightly more detailed discussion)

The Keynes Cross Model is a fairly simple way of presenting the Keynesian school of macroeconomics.  This belief system, which is a highly useful way of understanding the determination of the pace of total output in the economy, has been somewhat overshadowed by recent developments in macroeconomics.  It remains a valuable tool, and it can be more or less reduced to the following proposition:  the pace of activity in the economy is determined by the strength of the spending in the economy.  It is "demand side" macroeconomics.  It is not the whole story, but it is probably a good first approximation.   Here is a summary of the model.

            A.        Keynesian theory stresses the fact that  saving must  equal planned investment for an equilibrium to exist -- for the economy to be "at rest".

1.         The consumption function gives the relationship between income and the corresponding consumption:  the proportion of saving increases with income. i.e., if there is a low level of income in the economy a small fraction of income will be saved; but if income were to be greater, then the fraction saved would be larger.

                        2.         Investment as exogenous (lump sum), same for Gov't Spending

                        3.         With this scheme the level of GDP which will be attained is that where the amount produced equals the amount buyers are willing to buy (including investors, etc.) -- that requires Saving + Taxes = Investment + Government Spending (in terms of the circular flow model, leakages equal injections.)

                        4.         if the equilibrium GDP is not satisfactory, fiscal and monetary policy actions can be employed to bring about improvement.  Too low GDP can be remedied by expansionary policies. (What would they be?) Too high (inflationary) can be countered through contractionary policies.

 

Here are the details of the Keynesian cross:

VI. We will build the macroeconomic model called the Income-Expenditure Model -- the simple version of the Keynesian moddel.

B.         this model is attributable to J.M. Keynes  -- the most famous economist of this century.

            C.        a key feature (and a serious limitation) of this model is that prices are assumed to be constant -- which ties in with the concerns of the 1930s (employment, not prices).

D.        the income-expend. model is demand-based: it attempts to explain how total spending in the economy leads to the determination of some level of output (real GDP).  The spending in the economy is broken into its component parts.

                        1.         Beginning with consumption: Keynes believed that the main determinant of both consumption and saving is the level of income.

                                                            1) Specifically:

 

                                                                                        Income         Con   

                                                                                                  0             50    

                                                                                                100            100    

                                                                                                200            150    

                                                                                                300            200    

                                                                                                400            250    

                                                                                                500            300    

2)This can be plotted getting Consumption Function (income on horiz                                 axis, spending (here, consumption) on the vertical axis.

 

2.         Investment is second component of Aggregate Expenditure

a.         in reality investment varies depending on the level of income too, but will be ignored here

b.         also, investment is dependent on the rate of interest

1.         since we do not have the interest rate as one of the variable we are tracking (just spending and income), we will treat it as exogenous (determined outside of our system, a given).

2.         say it is 50 in this case (based on some int. rate).  Add 50 to consumption function (table)

3.         determinants of investment: profit expectations (outlook), technological change, tax policy, int. rate

3.         Government Purchases:  again take as independent of the level of income  (assume $50 bil). Add 50 (on table and graph)

a.         taxes:  simplifying, say the consumption function shown above is that which results after tax

4.         Net Exports: if our exports exactly are equal to our imports, the "foreign sector" has a neutral impact on our economy.  If there is an imbalance it can be a drain or a plus so far as our income and output go.  If net exports are positive it raises AE.  In the simplest case, net exports can be treated as exogenous (a constant).  A more realistic approach is to assume that net exports decrease at higher income (GDP) levels.

We now have the AE curve, which is C+I+G+NX   

6. Equilibrium requires that aggregate spending equals aggregate output.  Any other level of GDP, either higher or lower, is untenable since the spending is either more or less than output  -- leading to unplanned inventory accumulation if spending is too little, which will cause firms to slow down production, or spending is greater than output -- leading to inventory depletion and a speed-up of production.

 

VII.      Changes in equilibrium.  Any changes in autonomous components of spending, such as government spending, (as well as other possibilities) will change the equilibrium.

A.        AE shifts up or down, with new intersection with 45 degree.

B. That the change in income/output (that results from some shift of AE) is typically much larger than the change in AE (shift upward, say) is known as the multiplier.

1.         the multiplier in the simplest case, where the AE line is parallel to C, is simply  1/mps

a.         note that the greater the slope of AE, the greater the multiplier

                        2. more generally it is 1 / (1-slope of AE)